How? The thing is, they're not actually different numbers. They're just different ways of writing the same number.Quote:
Originally Posted by Kiloch
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How? The thing is, they're not actually different numbers. They're just different ways of writing the same number.Quote:
Originally Posted by Kiloch
Oh and I thought you understood. 1 = 0.999.... = 1 = 0.999.... How does that equate to 1 = 2 or 1 = 3? Just because 0.999.... = 1, it doesn't mean that .999... can equal some other number (unless that number is just another way of writing 1. For example cos 0 = 1, so .999... = cos 0).Quote:
Originally Posted by Kiloch
.999 is a numberQuote:
Originally Posted by boberman
cos 0 is an equation.
cos 0 is not an equation because it has a fixed value that will never change no matter what. Equations imply some variability to the expression (cos 0 is an expression, but so is .999...). For example, are you going to argue that sqr(1) is an equation? After all the square root operator is being called. how about 3/3 would that be an equation because the division operator is being called?Quote:
Originally Posted by Ejjman1
cos 0 is not an equation.
Even if it was, it wouldn't invalidate my argument in any way, shape or form because cos 0 always equates to 1, no matter what.
You've misunderstood me again. .999... is an undefined value (AFAIK). How can you equate two undefined values to each other?Quote:
Originally Posted by senrath
EDIT: At any rate, this one makes way less sense to me: e^(pi*sqrt -1) = -1.
.999... is not undefined. Is .333... Undefined? no. You seem to misunderstand what the term "Undefined" means. .999.. is very well defined, we know exactly how it behaves on to infinity. (just like .333... is very well defined)Quote:
Originally Posted by A G E N T
.999... behaves the same where ever it is placed and however it is used, just like 1 behaves the same in every situation it is placed in.
Nope.
If anyone isn't getting it, think about 2 things:
1) A number can have more than one representation.
2) If you can't deal with numbers going on forever, because it isn't what you're used to, look at the 1/3 proof posted by Ejjman
we use that repeating-decimal-to-fraction process to figure this out, no? so who's to say that that isnt wrong and that .999.... <> 1?...just wondering
That was ONE of the methods used to prove that .999... = 1, however it isn't the ONLY method used to prove it. There are several proofs using different methods of proving it true. Take a look at the wikipedia link. They have like 5 or six valid proofs of .999... = 1.Quote:
Originally Posted by Dan Cardin
Look, I've been thinking about this issue for a whole damn day straight now.
No matter how you put it, the difference between between 0.99.. and 1 will always remain as the 1^-..infinity (..0001). As long as there is some difference, the numbers aren't identical, and hence, 0.99.. is not the same as 1.
Nope.
Difference between 0.99 and 1 is 0.01. Difference between 0.999 and 1 is 0.001. Difference between 0.9999 and 1 is 0.0001. With each 9 you add, you add a 0 before you get to the 1. So if the 9s never stop, you never stop adding 0s, and you never get to the 1.
If you have an infinite number of digits, How do you tack a number on the end? You can't The 0s never end so the 1 never exists at the end. If the difference is infinitely small, it is non-existent.Quote:
Originally Posted by EvilChicken!
I +1 boberman's response.
If the 0's are infinite, there is no end. How can you put something on the end of something that doesn't end?
*cough* 9 minutes *cough* :pQuote:
Originally Posted by TViYH
Boberman, so by your logic any number with continuing digits = a different number simply because the .01 wouldn't have a chance to be placed is physical terms?
"If you have an infinite number of digits, How do you tack a number on the end? You can't The 0s never end so the 1 never exists at the end. If the difference is infinitely small, it is non-existent."
This logic goes against your algebra.
****_
So .89, by your logic must = .9 because that last digit would never be "tracked."
Algebra disproves this because
x = .8999...
10x = 8.999...
8.9 - x = 8.099...1, not .9 as with what happens with .99...
I am not here to disprove that .999... = 1. I simply saw a flaw in bober's logic, which implied that any repeating 9 = something larger.
Good point, I'd love to see an answer to this one.Quote:
Originally Posted by A G E N T
Brown: We're talking about .9, not .89.
A G E N T: To my knowledge, any number (positive) subtracted by itself is 0.
Algebra confirms it, if you do correct algebra, if you use incorrect algebra then you can say whatever you want, though it doesn't prove or disprove anything.Quote:
Originally Posted by Brown
First off, 8.9 - .89999 != 8.09991, it is equal to 8.00001. Therefore, 8.9 - .899.... is equal to, surprise 8. because that .8999.. is equivalent to saying .9.
Next time, check your algebra before saying it disproves anything. You can't say that there is a number at the end of an infinite sequence, by saying that you are saying your sequence isn't infinite. (infinite BY DEFINITION means never ending). A 1 after and infinite number of zeros doesn't exist because those zeros don't end. Heck, we might as well put pi, e, or ln(pi^e) in there, it doesn't matter because they don't exist.
Infinity is less of a number and more of a concept (a very strange concept the deeper you go into the rabbits hole, Look up cantor and his theories on infinity). If you don't have a cursory understanding on what infinity is and implies, then yes this won't make sense to you. However, you can trust me and every other person with a PHd in Mathematics that .999.... is in fact = 1.
10/3 = 3.33..
10/30 = .33..
.33.. x 3 = .99..
therefore..
3*10/30 = .99
30/30 = .99..
1/1 = .99..
1 = 0.99..
figured that mehord out my self :D
0.999... = 1 and 0.999... <> 1?
0.9 recurring can be proved by mathematically logical steps to be equal to 1
this has been known since the time of ancient greeks.
i dont even know why we're debating about this, its not anyones opinion, this is a mathematical fact, theres no room for debate or interpreting.
the only time I've ever debated against maths was satirically saying that pi = 3, which was only to point out the flawed attidute of religion.
pi equals three when I need to draw a sinus graph ^_^.